VIBRATION OF A SIMPLY SUPPORTED L-SHAPED PLATE

Recently Solecki (1996) has shown that a differential equation for vib ration of a rectangular plate with a cutout can be reduced to boundary integral equations. This was accomplished by filling the cutout with a ''patch'' made of the same material as the rest of the plate and sep arated from it by an infinitesimal gap. Thanks to this procedure it wa s possible to apply finite Fourier transformation of discontinuous fun ctions in a rectangular domain. Subsequent application of the availabl e boundary conditions led to a system of boundary integral equations. A plate simply supported along the perimeter, and fixed along the cuto ut (an L-shaped plate), was analyzed as an example. The general soluti on obtained by Solecki (1996) serves here to determine the frequencies of natural vibration of a L-shaped plate simply supported all around its perimeter. This problem is, however, more complicated than the pre vious example: to satisfy the boundary conditions an infinite series d epending on discontinuous functions must be differentiated The theoret ical development is illustrated by numerical values of the frequencies of the natural vibrations of a square plate with a square cutout. The results are compared with the results obtained using finite elements method.